4x^2+5x-45=0

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Solution for 4x^2+5x-45=0 equation:


Simplifying
4x2 + 5x + -45 = 0

Reorder the terms:
-45 + 5x + 4x2 = 0

Solving
-45 + 5x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-11.25 + 1.25x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + 1.25x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + 1.25x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + 1.25x + x2 = 0 + 11.25
1.25x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
1.25x + x2 = 11.25

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 11.25 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 11.25 + 0.390625

Combine like terms: 11.25 + 0.390625 = 11.640625
0.390625 + 1.25x + x2 = 11.640625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 11.640625

Calculate the square root of the right side: 3.411836016

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.411836016 and -3.411836016.

Subproblem 1

x + 0.625 = 3.411836016 Simplifying x + 0.625 = 3.411836016 Reorder the terms: 0.625 + x = 3.411836016 Solving 0.625 + x = 3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.411836016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.411836016 + -0.625 x = 3.411836016 + -0.625 Combine like terms: 3.411836016 + -0.625 = 2.786836016 x = 2.786836016 Simplifying x = 2.786836016

Subproblem 2

x + 0.625 = -3.411836016 Simplifying x + 0.625 = -3.411836016 Reorder the terms: 0.625 + x = -3.411836016 Solving 0.625 + x = -3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.411836016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.411836016 + -0.625 x = -3.411836016 + -0.625 Combine like terms: -3.411836016 + -0.625 = -4.036836016 x = -4.036836016 Simplifying x = -4.036836016

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.786836016, -4.036836016}

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